EXPERIMENT 7 - THE ENTHALPY OF HYDRATION
OBJECTIVE
To determine the enthalpy of hydration, Hhydration, for the
reaction
Na2CO3 (s) + 10 H2O (l)  Na2CO310H2O (s)
Hhydration = ?
rxn (7-1)
THEORY
Chemical thermodynamics deals with energy changes which accompany chemical
reactions. Thermochemistry deals with energy changes manifested as heat of reaction at
constant pressure, H. A reaction is said to be exothermic if heat is lost by the reactants
to the surroundings. Under this condition H is assigned a negative value. Conversely, a
reaction which is endothermic has a H which is assigned a positive value. From a
theoretical point of view, H is important because it determines, in part, the design and
operating economic feasibility of a process.
In general terms, enthalpy of reaction, may be subdivided into enthalpy of combustion,
enthalpy of vaporization, fusion, and so on. In this experiment we are concerned with the
enthalpy of solution and the enthalpy of hydration.
Hess' Law states that H for a reaction is independent of the number of steps of the path
by which a reaction is carried out. Its validity is a direct consequence of the First Law of
Thermodynamics.
An example of an application of Hess' Law is illustrated in the following example.
Suppose we wish to know H for the following reaction:
Mg (s) + 2 HCl (g)  MgCl2 (s) + H2 (g)
H = ?
rxn (7-2)
Mg (s) + Cl2 (g)  MgCl2 (s)
H = - 640 kJ
rxn (7-3)
½ H2 (g) + ½ Cl2 (g)  HCl (g)
H = - 92 kJ
rxn (7-4)
Suppose the following information is available:
and
We can obtain rxn (7-2) by multiplying rxn (7-4) by 2 and subtracting it from rxn (7-3).
The value of H is obtained in the same way. Thus H for rxn (7-2) is
Hrxn (7-2) = - 640 - 2(-92) = -456 kJ
7-1
The example shows that if H for a given reaction cannot be readily determined, it can be
found by replacing the desired reaction with a series of equivalent reactions whose
enthalpies are known or can be readily determined from calorimetry. There are two
precautions to be observed with calorimetry. The first is dealing with the problem of heat
transfer between calorimeter and surroundings. In precision analysis, an adiabatic
calorimeter is used. Such a calorimeter has two insulating jackets in which the outer
jacket is automatically maintained at the same temperature as the calorimeter. For less
precise work, a Dewar flask or even a plastic container can be used to minimize the heat
transfer between the calorimeter and surroundings.
The second problem is to determine the heat capacity of the calorimeter (ie - amount of
heat energy required to raise its temperature by one degree). In one method, a known
quantity of electrical energy is supplied to the calorimeter. In the second method a known
amount of a liquid at elevated temperataure is mixed with the contents in the flask. In
both cases, a temperature change is observed in the calorimeter and its contents.
In this experiment, you will be determining the Hhydration of the following reaction:
Na2CO3 (s) + 10 H2O (l)  Na2CO310H2O (s)
rxn (7-1)
Since the Hhydration of rxn (7-1) cannot be measured directly, we will apply Hess' Law
and measure Hhydration for this reaction indirectly.
7-2
PROCEDURE NB - All glassware has to be CLEAN and DRY.
The Dewar flask has to be CLEAN and DRY.
[Do not use acetone or air to dry the Dewar flask. Use paper towel to dry
the inside thoroughly.]
Part A - Determination of the heat capacity of the calorimeter, Ccal
1.
Using a buret, dispense 50.00 mL distilled water in a clean and dry 125 mL
Erlenmeyer flask and heat the flask and its contents in a water bath at 40o- 50oC.
2.
Allow the Erlenmeyer flask to reach thermal equilibrium and measure the
temperature of the flask by dipping thermometer in the water bath next
to the flask. Record the water bath temperature on the data sheet for Part A, B,
and C. DO NOT dip thermometer in the flask as you do not want to remove
any water from the flask.
[Use the same thermometer to measure ALL subsequent temperatures
in this experiment].
3.
Using a buret, dispense another 50.00 mL portion of distilled water at room
temperature into a Dewar flask. Gently push the thermometer (the same one
used in step 2) through the hole of the rubber stopper. Make sure the thermometer
is positioned so that the thermometer bulb is immersed in the water. Seal the
Dewar flask with the rubber stopper.
4.
Record temperatures inside the Dewar flask at 60 second intervals for 180
seconds.
5.
At time = 240 sec, pour the warm distilled water into the calorimeter. Replace the
rubber stopper/thermometer assembly on the calorimeter and gently swirl the
mixture. Do not let the thermometer bang against the side of the calorimeter.
The temperature in the flask will rise quickly to a maximum and begin to fall
slowly.
Do not try to take a temperature reading at time = 240 sec. This point is obtained
by extrapolation on the graph.
6.
Record temperatures inside the Dewar flask at time = 300, 360, 420, 480, 540, and
600 seconds.
7-3
Part B - Determination of Enthalpy of Solution of Na2CO310 H2O
1.
Using a buret, dispense in 50.00 mL distilled water in a clean and dry 125 mL
Erlenmeyer flask and heat the flask and its contents in a water bath at 40o- 50oC.
2.
Weigh 12.00  0.01 g of sodium carbonate decahydrate into the clean and dry
calorimeter (ie - the same Dewar flask used in Part A). Record the mass on the
data sheet.
3.
Place the sodium carbonate decahydrate inside the calorimeter and, with
the rubber stopper/thermometer assembly in place, measure the temperature
inside the Dewar flask at 60 seconds intervals for 180 seconds. Record the
temperature measurements on the data sheet.
Note: The thermometer does not have to be touching the solid.
4.
At time = 240 sec, pour the warm distilled water into the calorimeter. Replace the
rubber stopper/thermometer assembly on the calorimeter and gently swirl the
mixture. Do not let the thermometer bang against the side of the calorimeter.
Note: You should peek inside to that all the solid has dissolved.
Do not try to take a temperature reading at time = 240 sec. This point is obtained
by extrapolation on the graph.
5.
Record temperature of the mixture at time = 300, 360, 420, 480, 540, and 600
seconds.
7-4
Part C - Determination of Enthalpy of Solution of anhydrous Na2CO3
1.
Using a buret, dispense 57.50 mL distilled water into a clean and dry 125 mL
Erlenmeyer flask and heat the water to 40o - 50o C. The extra 7.5 mL water is the
amount of water used to hydrate anhydrous Na2CO3.
2.
*Weigh out 4.50  0.01 g of anhydrous sodium carbonate into the clean and
dry calorimeter (same Dewar flask as in Parts A and B). Record the mass on the
data sheet.
** Do not weigh out your anhydrous sodium carbonate ahead of time. The solid will
absorb water from the atmosphere.
3.
Place the anhydrous sodium carbonate inside the calorimeter and, with
the rubber stopper/thermometer assembly in place, measure the temperature
inside the Dewar flask at 60 seconds intervals for 180 seconds. Record the
temperature measurements on the data sheet.
Note: The thermometer does not have to be touching the solid.
4.
At time = 240 sec, pour the warm distilled water into the calorimeter. Replace the
rubber stopper/thermometer assembly on the calorimeter and gently swirl the
mixture. Do not let the thermometer bang against the side of the calorimeter.
Note: You should peek inside to that all the solid has dissolved.
Do not try to take a temperature reading at time = 240 sec. This point is obtained
by extrapolation on the graph.
5.
Record temperature of the mixture at time = 300, 360, 420, 480, 540, and 600
seconds.
7-5
DATA SHEET
Part A - Determination of the heat capacity of the calorimeter, Ccal
Water bath temperature (thigh) : ___________________________
Table (7-1) - Data for the determining the heat capacity of the calorimeter.
Time (sec)
Temperature (oC)
0
60
120
180
240
teq and tlow are obtained by
extrapolation
300
360
420
480
540
600
7-6
Part B - Determination of Enthalpy of Solution of Na2CO310 H2O
Na2CO310H2O (s)  Na2CO3 (aq) + 10 H2O (l)
H1 = ?
rxn (7-5)
Water bath temperature (thigh) : ___________________________
Mass of Na2CO310 H2O: ______________________________
Table (7-2) - Data for determining H1.
Time (sec)
Temperature (oC)
0
60
120
180
240
teq and tlow are obtained by
extrapolation
300
360
420
480
540
600
7-7
Part C - Determination of Enthalpy of Solution of anhydrous Na2CO3
Na2CO3 (s)  Na2CO3 (aq)
H2 = ?
rxn (7-6)
Water bath temperature (thigh) : ___________________________
Mass of Na2CO3: _____________________________________
Table (7-3) - Data for determining H2.
Time (sec)
Temperature (oC)
0
60
120
180
240
teq and tlow are obtained by
extrapolation
300
360
420
480
540
600
7-8
INTERPRETATION OF DATA Part A - Determination of the heat capacity of the calorimeter, Ccal
In Part A, you will be measuring the heat capacity of the calorimeter (or Dewar flask).
Since you will be using the same calorimeter in Parts B and C, the amount of heat
absorbed by the calormeter will be the same each time.
If m2 grams of water at temperature thigh is added to m1 grams of water inside a
calorimeter at temperature tlow, the warm water loses heat to the cool water and the
calorimeter. The amount of heat that is lost by the warm water must equal the heat gained
by the cool water and the calorimeter. In other words,
Heat lost = Heat gained
heat lost by hot water = heat gained by cold water + heat gained by calorimeter.
Eventuallly inside the calorimeter, an equilibrium temperature, teq, will be achieved.
Mathematically, we can express this as follows:
cwater m2 (thigh - teq) = cwater m1 (teq - tlow) + Ccal (teq - tlow)
eqn (7-1)
where cwater = specific heat of water (Joules g-1 deg-1),
Ccal = heat capacity of calorimeter (Joules deg-1)
By plotting a graph of "Temperature versus time " , tlow and teq can be found by
extrapolation (see Figure (7-1)).
7-9
Figure (7-1) - tlow and teq can be determined by extrapolation
of a graph of "Temperature versus time"
Solve eqn (7-1) for ' Ccal ', and the heat capacity of the calorimeter can be easily
determined.
Part B - Determination of Enthalpy of Solution of Na2CO310 H2O
In Part B, you will be determining the enthalpy of solution of
Na2CO310 H2O. The chemical reaction is as follows:
Na2CO310H2O (s)  Na2CO3 (aq) + 10 H2O (l)
H1 = ?
rxn (7-5)
m2 grams of water at temperature thigh is added to w1 grams of Na2CO310 H2O
inside a calorimeter at temperature tlow. Again,
Heat lost = Heat gained
heat lost
heat gained
by
=
by
+
warm water
calorimeter
heat gained
by the 10 moles +
of water released
heat
of
solution
Eventuallly inside the calorimeter, an equilibrium temperature, teq, will be achieved.
Mathematically, we can express this as follows:
cwater m2 (thigh - teq) = Ccal (teq - tlow) + cwater w1(180/286) (teq - tlow) + q1
eqn (7-2)
7-10
where q1 is the heat of solution of Na2CO310 H2O.
Once the heat of solution, q1, is determined, the molar heat of solution of
Na2CO310H2O, H1 can be calculated using eqn (7-3).
H1 =
FW(Na2 CO3  10 H 2 O)
 q1
w1
eqn (7-3)
where FW (Na2CO310 H2O) is the formula weight of Na2CO310 H2O.
Part C - Determination of Enthalpy of Solution of anhydrous Na2CO3
In Part C, you will be determining the enthalpy of solution of anhydrous, Na2CO3. The
chemical reaction is as follows:
Na2CO3 (s)  Na2CO3 (aq)
H2 = ?
rxn (7-6)
m2 grams of water at temperature thigh is added to w2 grams of anhydrous
Na2CO3 inside a calorimeter at temperature tlow. Again,
Heat lost = Heat gained
heat lost
heat gained
by
=
by
+
warm water
calorimeter
heat
of
solution
Eventuallly inside the calorimeter, an equilibrium temperature, teq, will be achieved.
Mathematically, we can express this as follows:
cwater m2 (thigh - teq) = Ccal (teq - tlow) + q2
eqn (7-4)
where q2 is the heat of solution of anhydrous Na2CO3.
Once the heat of solution, q2, is determined, the molar heat of solution of anhydrous
Na2CO3, H2 can be calculated using eqn (7-5).
H 2 =
FW(Na2 CO3 )
 q2
w2
eqn (7-5)
where FW (Na2CO3) is the formula weight of Na2CO3.
Recall, the object of the experiment is to determine the enthalpy of hydration,
Hhydration, for the reaction
Na2CO3 (s) + 10 H2O (l)  Na2CO310H2O (s)
Hhydration = ?
7-11
rxn (7-1)
We can now use Hess' Law to calculate Hhydration, the heat of hydration for
Na2CO3. This is achieved by utilizing your experimental data. Combine your results for
H1 and H2 in the correct manner to produce a value for Hhydration.
A theoretical value of Hhydration can be calculated if the heats of
formation, Hfo, of Na2CO310 H2O (s), Na2CO3 (s) and H2O (l) are known. Hfo
can be looked up from reference books.
Hhydration =  Hfo(products) -  Hfo (reactants)
eqn (7-6)
Therefore,
Hhydration = Hfo(Na2CO310 H2O (s)) - ( Hfo(Na2CO3 (s)) +10 Hfo(H2O (l)).
eqn (7-7)
7-12
TREATMENT OF DATA
Graphing
Plot separate graphs of "Temperature verse time" for each part of the experiment.
Calculations
From each graph extropolate values for tlow and teq.
Part A - Calculation of the Heat Capacity, Ccal
(i)
Use eqn (7-1) to calculate the heat capacity of the calorimeter, Ccal.
Part B - Calculation of q1, the heat of solution of Na2CO310 H2O
(i)
Use eqn (7-2) to calculate q1, the heat of solution for w1 grams of
Na2CO310 H2O.
(ii)
Use eqn (7-3) to calculate H1, the molar heat of solution of
Na2CO310 H2O.
Part C - Calculations of q2, the heat of solution of anhydrous Na2CO3
(i)
Use eqn (7-4) to calculate q2, the heat of solution for w2 grams of
Na2CO3.
(ii)
Use eqn (7-5) to calculate H2, the molar heat of solution of Na2CO3.
Questions
1.
In the space provided, use Hess' Law to calculate Hhydration to rxn (7-1) by
combining your results for H1 and H2 in the correct manner.
2.
In the space provided, calculate a theoretical value of Hhydration for rxn (7-1).
3.
In the space provided, calculate the % error of Hhydration.
7-13
Calculations
Part A - Calculation of the Heat Capacity, Ccal
cwater m2 (thigh - teq) = cwater m1 (teq - tlow) + Ccal (teq - tlow)
eqn (7-1)
cwater
4.18 J/g oC
m1
50.00 g
m2
thigh
tlow
teq
Heat capacity of calorimeter
7-14
Part B - Calculation of q1, the heat of solution of Na2CO310 H2O
cwater m2 (thigh - teq) = Ccal (teq - tlow) + cwater w1(180/286) (teq - tlow) + q1
eqn (7-2)
H1 =
FW(Na2 CO3  10 H 2 O)
 q1
w1
cwater
eqn (7-3)
4.18 J/g oC
Ccal
m2
50.00 g
w1
thigh
tlow
teq
q1
H1
7-15
Part C - Calculations of q2, the heat of solution of anhydrous Na2CO3
cwater m2 (thigh - teq) = Ccal (teq - tlow) + q2
H 2 =
FW(Na2 CO3 )
 q2
w2
cwater
eqn (7-4)
eqn (7-5)
4.18 J/g oC
Ccal
m2
57.50 g
w2
thigh
tlow
teq
q2
H2
7-16
Questions
1.
Calculation of Hhydration of
Na2CO3 (s) + 10 H2O (l)  Na2CO310H2O (s)
rxn (7-1)
Determination of Hhydration for the above reaction using Hess' Law.
Hhydrationo (experimental)
7-17
2.
Calculate the theoretical value of Hhydration.
Reference source for Hfo = _______________________________
Substance
Hfo
Na2CO310 H2O (s)
Na2CO3 (s)
H2O (l)
Hhydrationo (theoretical)
7-18
3.
Calculate the % error of Hhydration.
7-19